Is a team only as strong as its weakest link?

Yes. Team trust is not determined by an average of the members, it’s at the level of the least trusted member:

In a team negotiation context, the authors empirically explored how judgments of team-level trust are derived from individual-level trust. Basing their argument on both the negativity bias and the discontinuity effect, the authors posit that people will focus most on the least trustworthy individual member of a team when making judgments about collective team-level trust. Findings from two studies demonstrate that perceptions of team trust are indeed lower than the average ratings of individual trust and are statistically equivalent to the least trusted member. In addition, compared with average individual trust levels, perceptions of collective team trust were found to be more predictive of (a) impasse rates in distributive negotiations and (b) the level of joint gain in integrative negotiations.